Computability and Logic |
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Editorial Review / Publisher's Information:
Product Description
Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, such as Godel's incompleteness theorems, but also a large number of optional topics, from Turing's theory of computability to Ramsey's theorem. Including a selection of exercises, adjusted for this edition, at the end of each chapter, it offers a new and simpler treatment of the representability of recursive functions, a traditional stumbling block for students on the way to the Godel incompleteness theorems.
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Customer Reviews:
• Could Be Much Better
21 March, 2009
This book has so much going for it: eminent authors, great coverage, lots of exercises and it's quite inexpensive for a math book. But it also has some major drawbacks. First of all: the typos. Oh the typos. I've seen reviews for the fourth edition where there were lots of complaints about the typos. This (the fifth edition) may be an improvement but there are still way too many typos. A bigger problem is that the authors don't always make the important conceptual connections between the material explicit - and this may be the result of a book written by committee. To give an example, there is a whole chapter on enumerability with no mention of decidability. When the authors finally introduce decidability sixty pages later it is not clearly compared with enumerability. But these concepts are related in a very simple but important way - something a beginning student would not realize on reading this book. Finally, the authors don't do a good job of presenting the *big picture* in mathematical logic. And without that, it makes the material less interesting and more difficult to learn.
- Amazon Customer Review
• Very Good Textbook
10 October, 2009
I grew up with earlier editions of this book and now teach from it. It's an excellent introduction to this material, pitched at just the right level, in my experience, for its intended audience. For students (or people in general) who are extremely sophisticated mathematically, it can sometimes seem a little unrigorous. But for my students, who are mostly philosophers, it manages to convey a sense for what is going on without overdoing it on the detail. This is not to say that it does not get rigorous where necessary. It does. But when that's not critical, it's content to leave things at a more intuitive level.
As far as approach is concerned, the book places recursion theory at the center. The first several chapters introduce the basics of this subject, and only then do the authors turn toward theories of arithmetic and the like. This corresponds to what is probably the dominant way of thinking of Goedel's theorem: that, at its core, it is a theorem in recursion theory.
Other topics are covered along the way, too, of course, and there are several different courses one could teach using this book. The selection of problems is good, too.
- Amazon Customer Review
• Worked For Class
25 February, 2010
My professor uses this book to the last word. It's a good book overall however the content is not exactly easy. I would recommend this for someone who has a little knowledge of the subject. A novice could possibly use it with the help of google.
- Amazon Customer Review
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